Persistent links are called "permalinks" in the EBSCO databases.
Not all articles in the EBSCO databases are available in full-text. Try clicking the Full Text Finder link to see if it is available elsewhere. If so, use that URL as a permalink. Creating a persistent link only works for articles available in full-text in the EBSCO database.
After you run a search in the database, click on the title of the article and click on the "permalink" icon on the right side of the screen.
Copy the URL in the Permalink text box. Add the Permalink into Brightspace as directed in the Brightspace documentation. You do not need to add any proxy information.
The complete list of EBSCOhost databases that SUNY Cortland has access to is ever-changing. However, here are a few examples: